An equalizer is a filter that removes from a received signal the amplitude and phase distortions that result from the frequency dependent time-variant response of the transmission channel. The objective of an equalizer is to process a received signal and output a representation of the original transmitted signal. Equalizers effect this result by emulating the transfer function of the transmission channel and applying the inverse of the transfer function to the received signal so as to remove the distortion. The equalizer isolates the data symbols of the received signal and and corrects the associated time dependent distortion affects. However to design an equalizer to work as described, the transfer function of the transmission channel must be known and stable; in application neither is true. Therefore, equalizers have been developed that learn the transfer function of the transmission channel. These equalizers are known in the art as adaptive equalizers.
There are two important measures of performance to consider in adaptive equalizer design, the speed of adaption and the accuracy of the learned transfer function. Generally there is a trade-off between these two criteria. To achieve a more accurate transfer function requires a longer adaption period. The penalty for a longer adaption period is a communications channel that remains closed while the equalizer is adapting. For the first equalizer applications, the accuracy of the adaption algorithm was critical, with the speed of convergence less so. The reason was the transmission speeds employed were limited and therefore the frequencies to be equalized were limited and the required convergence calculations were not a problem. New transmission technologies operate at greater transmission speeds requiring higher bandwidths which result in ever more complex filters with ever longer convergence times. Therefore, the speed of convergence becomes a design issue. The method of convergence, "convergence algorithm", has a significant impact on convergence time.
A conventional algorithm such as the Least Mean Squared (LMS) algorithm takes hundreds of iterations to converge although it is easy to implement and robust. Other convergence algorithms exists that are capable of converging in fewer iterations but they are computationally intensive for each iteration, and therefore expensive to implement. As a result the LMS algorithm has been used for many practical applications.
The convergence property of adoptive algorithms has been studied using vector space theory in the context of some fast algorithms by M. L. Honig ("Recursive fixed-order covariance Least-Squares algorithms," Bell System Technical Journal, vol. 62 No. 10, pp 2961-2992, December 1983). It was found there that the convergence speed depends on the ratio of the maximum to minimum eigenvalues of the received signal's autocorrelation matrix. The eigenvalue spread is minimized when the received signal is white and therefore the ratio of the maximum to minimum eigenvalues approach one. As the ratio approaches one, the speed of convergence increases. Most existing fast algorithms apply a signal whitening process only to the received signal but not to the original signal, or equivalently, to the decision output for the equalizing application.
For the LMS algorithm the convergence speed is fastest when the received signal is white. If the received signal is not white other fast algorithms, such as the Kalman or Lattice, which effectively perform received signal whitening during convergence can be used. However, these algorithms are complex and expensive to implement.
Therefore, in view of the foregoing it is an object of the present invention to provide a method and apparatus to increase the convergence speed of an adaptive filter employing the Least Mean Squared algorithm.